Walking Takahashi

Takahashi, who lives on the number line, is now at coordinate X. He will make exactly K moves of distance D in the positive or negative direction.

More specifically, in one move, he can go from coordinate x to x + D or x - D.

He wants to make K moves so that the absolute value of the coordinate of the destination will be the smallest possible.

Find the minimum possible absolute value of the coordinate of the destination.

Constraints

• -10^{15} \leq X \leq 10^{15}
• 1 \leq K \leq 10^{15}
• 1 \leq D \leq 10^{15}
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

X K D

Output

Print the minimum possible absolute value of the coordinate of the destination.

Examples

Input

6 2 4

Output

2

Input

7 4 3

Output

1

Input

10 1 2

Output

8

Input

1000000000000000 1000000000000000 1000000000000000

Output

1000000000000000

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

X K D

outputFormat

Output

Print the minimum possible absolute value of the coordinate of the destination.

Examples

Input

6 2 4

Output

2

Input

7 4 3

Output

1

Input

10 1 2

Output

8

Input

1000000000000000 1000000000000000 1000000000000000

Output

1000000000000000

样例

1000000000000000 1000000000000000 1000000000000000

1000000000000000